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Given this pair of slopes, what is the value of n if the lines are parallel? What is the value of n if the lines are perpendicular?

 

\({3 \over n}\),\(-{7 \over 2}\)

 

If I cross multiply, the parallel slope is \(n = -{6 \over 7}\), is that right?

As for perpendicular... how would I solve for that?

Guest Apr 8, 2018
 #1
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Parallel lines have the same slope.

 

If the lines are parallel, then the slopes of the lines are equal.

 

If the lines area parallel, then....

 

\(\frac3n\,=\,-\frac72 \\~\\ 3\cdot2\,=\,-7\cdot n \\~\\ 6\,=\,-7n\\~\\ n\,=\,-\frac67\)

 

....You're right!!! laugh

 

If the lines are perpendicular, then the slopes are negative reciprocals of each other.

 

That means   \(\frac3n\)   must equal the negative reciprocal of   \(-\frac72\)  .

 

The negative reciprocal of   \(-\frac72\)   is    \(\frac27\)  .

 

If the lines are perpendicular, then....

 

\(\frac3n\,=\,\frac27\\~\\ 7\cdot3\,=\,2\cdot n\\~\\ 21\,=\,2n\\~\\ n\,=\,\frac{21}{2}\)

hectictar  Apr 8, 2018

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